Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, G

Average Accuracy: 100.0% → 100.0%

Time: 1.2s

Precision: binary64

Cost: 320

Math

\[\frac{1}{2} \cdot \left(x + y\right) \]

↓

\[0.5 \cdot \left(x + y\right) \]

FPCore

(FPCore (x y) :precision binary64 (* (/ 1.0 2.0) (+ x y)))

↓

(FPCore (x y) :precision binary64 (* 0.5 (+ x y)))

C

double code(double x, double y) {
	return (1.0 / 2.0) * (x + y);
}

↓

double code(double x, double y) {
	return 0.5 * (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 / 2.0d0) * (x + y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * (x + y)
end function

Java

public static double code(double x, double y) {
	return (1.0 / 2.0) * (x + y);
}

↓

public static double code(double x, double y) {
	return 0.5 * (x + y);
}

Python

def code(x, y):
	return (1.0 / 2.0) * (x + y)

↓

def code(x, y):
	return 0.5 * (x + y)

Julia

function code(x, y)
	return Float64(Float64(1.0 / 2.0) * Float64(x + y))
end

↓

function code(x, y)
	return Float64(0.5 * Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 / 2.0) * (x + y);
end

↓

function tmp = code(x, y)
	tmp = 0.5 * (x + y);
end

Wolfram

code[x_, y_] := N[(N[(1.0 / 2.0), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision]

Target

Original	100.0%
Target	100.0%
Herbie	100.0%

\[\frac{x + y}{2} \]

Derivation

1. Initial program 100.0%

   \[\frac{1}{2} \cdot \left(x + y\right) \]

2. Simplified 100.0%

   \[\leadsto \color{blue}{0.5 \cdot \left(x + y\right)} \]
   Step-by-step derivation

   [Start] 100.0	\[ \frac{1}{2} \cdot \left(x + y\right) \]
   metadata-eval [=>] 100.0	\[ \color{blue}{0.5} \cdot \left(x + y\right) \]

3. Final simplification 100.0%

   \[\leadsto 0.5 \cdot \left(x + y\right) \]

Reproduce

herbie shell --seed 2023157 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, G"
  :precision binary64

  :herbie-target
  (/ (+ x y) 2.0)

  (* (/ 1.0 2.0) (+ x y)))